Sum Data by Month & Category

I have used a sumifs()
But had to change your titles of months from TEXT to an actual date 1st jan 2021 for example and then used a format MMMM to just show the month as you had it
=SUMIFS($F$3:$F$7,$E$3:$E$7,$C11,$B$3:$B$7,">="&D$10,$B$3:$B$7,"<="&EOMONTH(D$10,0))
But also added a pivot table, just to show how it can be setup with a pivot table, which can be quicker and gives some more options